A task-driven network for mesh classification and semantic part segmentation

Given the rapid advancements in geometric deep-learning techniques, there has been a dedicated effort to create mesh-based convolutional operators that act as a link between irregular mesh structures and widely adopted backbone networks. Despite the numerous advantages of Convolutional Neural Networks (CNNs) over Multi-Layer Perceptrons (MLPs), mesh-oriented CNNs often require intricate network architectures to tackle irregularities of a triangular mesh. These architectures not only demand that the mesh be manifold and watertight but also impose constraints on the abundance of training samples. In this paper, we note that for specific tasks such as mesh classification and semantic part segmentation, large-scale shape features play a pivotal role. This is in contrast to the realm of shape correspondence, where a comprehensive understanding of 3D shapes necessitates considering both local and global characteristics. Inspired by this key observation, we introduce a task-driven neural network architecture that seamlessly operates in an end-to-end fashion. Our method takes as input mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles between adjacent faces. Notably, we replace the conventional convolutional module, commonly found in ResNet architectures, with MLPs and incorporate Layer Normalization (LN) to facilitate layer-wise normalization. Our approach, with a seemingly straightforward network architecture, demonstrates an accuracy advantage. It exhibits a marginal 0.1% improvement in the mesh classification task and a substantial 1.8% enhancement in the mesh part segmentation task compared to state-of-the-art methodologies. Moreover, as the number of training samples decreases to 1/50 or even 1/100, the accuracy advantage of our approach becomes more pronounced. In summary, our convolution-free network is tailored for specific tasks relying on large-scale shape features and excels in the situation with a limited number of training samples, setting itself apart from state-of-the-art methodologies.